That is a 1.5" IPT pipe at both ends. The middle of it is wider because it is length adjustable; two pipes that nest inside each other. The part that threads into the PRG-UNV and the part that threads into the tile bridge/ceiling plate is standard 1.5" IPT pipe.

I'm going to assume based on the reference to ceiling tile that you are going in a 2x2 or 2x4 drop ceiling with a grid?

I'm also going to assume that based on the weight capacity of the mount you mentioned that the projector you are installing is under 50 lbs?

If so, why not just use a tile bridge drop ceiling mounting kit? It would be faster and easier than like a unistrut substructure or piping directly to deck (the only way that wider section of pipe wouldn't be below the ceiling).

As an added bonus most of the kits include an escutcheon ring, which is indeed the trade name for the trim part you referenced, in the correct size if the parts are used as intended.

I don't know Peerless as well, but with like a Chief CMS-440 (which you could use with the rest of your peerless parts, 1.5" IPT is a standard), they even include a little tool to help neatly cut the exact right size hole in the tile for the included escutcheon ring, which coincidentally is also the correct size for a 1.5" IPT pipe to pass-through and made to neatly cut ceiling tile.

That also allows you to locate the projector without the ceiling tile, mark out where the bridge should sit in the grid, put the tile back and use the hole in the bridge as a template to get the hole in the right spot if it has to be exact and/or just move the bridge a little if your hole is off a little. Leave the cables loose until everything is in place, then pull tight to pull the weight off the grid. No guessing where the hole needs to be (otherwise use a plumb bob).

Further, you probably don't need 6-9" of adjustability at that point, more like a 3" or 6" fixed pipe, which eliminates that issue with the bump in the middle and looks nicer anyway.

Why not just buy the right parts to do it correctly instead of trying to reinvent the wheel?